+0  
 
0
2
1
avatar+1121 

For certain values of $k$ and $m,$ the system
a + 2b = -3 - 7a + b,
4a + 2b = k - 5a - mb
has infinitely many solutions $(a,b).$ What are $k$ and $m?$

 May 10, 2024
 #1
avatar+128796 
+1

Rearrange as

 

8a + b =  -3       (1)

9a + (2 + m)b = k     (2)

 

This system has infinite solutions when the equations are the  same

Multiply (1) by 9  and (2) by 8

 

72a  + 9b = -27

72a + 8(2 + m)b  = 8k

 

So

 

9 =  8(2+m)                  -27  =   8k

9 = 16 + 8m                   k = -27/8

8m  = -7

m = -7/8 

 

cool cool cool

 May 10, 2024

3 Online Users